Cryptology ePrint Archive: Report 2012/680

Natural Generalizations of Threshold Secret Sharing

Oriol Farras,Carles Padro,Chaoping Xing, and An Yang

Abstract: We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit an ideal linear secret sharing schemes over
every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure
the proofs for the existence of ideal secret sharing schemes for them.